ProbitModelFit returns a symbolic FittedModel object to represent the probit model it constructs. The properties and diagnostics of the model can be obtained from model["property"].

The value of the best-fit function from ProbitModelFit at a particular point x1, … can be found from model[x1,…].

With data in the form {{x11,x12,…,y1},{x21,x22,…,y2},…}, the number of coordinates xi1, xi2, … should correspond to the number of variables xi.

The yi are probabilities between 0 and 1.

Data in the form {y1,y2,…} is equivalent to data in the form {{1,y1},{2,y2},…}.

ProbitModelFit produces a probit model under the assumption that the original are independent observations following binomial distributions with mean .

In ProbitModelFit[{m,v}], the design matrix m is formed from the values of basis functions fi at data points in the form {{f1,f2,…},{f1,f2,…},…}. The response vector v is the list of responses {y1,y2,…}.

For a design matrix m and response vector v, the model is where is the vector of parameters to be estimated.

When a design matrix is used, the basis functions fi can be specified using the form ProbitModelFit[{m,v},{f1,f2,…}].